Question

(а+3b/a^2-3ab-1/a):b/3b-a

Answer 1

((а+3b)/(a^2-3ab)-1/a)×(3b-a)/b=
((a+3b)/a(a-3b)-1/a)×(3b-a)/b=
((a+3b-a+3b)/a(a-3b))×-(a-3b)/b=
-(6b/a(a-3b)×(a-3b)/b=-6/a=-6:-16/10=
-6×-10/16=3×5/4=15/4=3 3/4=3,75

 

Answer 2

To simplify the given expression, let's break it down step by step.

Expression: (а + 3b/a^2 - 3ab - 1/a) : b/3b - a

Step 1: Simplify the numerator of the fraction inside the parentheses. The numerator of the fraction is (a + 3b).

Expression: (a + 3b/a^2 - 3ab - 1/a) : b/3b - a

Step 2: Simplify the denominator of the fraction inside the parentheses. The denominator of the fraction is (a^2 - 3ab - 1/a).

Expression: (a + 3b)/(a^2 - 3ab - 1/a) : b/3b - a

Step 3: Simplify the expression inside the parentheses. Since there is only one term in the numerator and denominator, we can rewrite it as a fraction.

Expression: (a + 3b) / ((a^2 - 3ab - 1) / a) : b/3b - a

Step 4: Invert the second fraction and multiply it with the first fraction. Inverting a fraction involves swapping the numerator and denominator.

Expression: (a + 3b) / ((a^2 - 3ab - 1) / a) * (3b - a) / b

Step 5: Simplify the expression further by canceling out common factors if possible. Notice that (3b - a) / b can be simplified to 3 - (a / b).

Expression: (a + 3b) * (3 - (a / b)) / ((a^2 - 3ab - 1) / a)

Step 6: Simplify the expression inside the parentheses further by distributing.

Expression: (3a + 9b - a^2 / b) / ((a^2 - 3ab - 1) / a)

At this point, the expression cannot be simplified any further unless specific values are assigned to the variables a and b.